@@ -192,8 +186,43 @@

alt

-

Multidimensional 0-1 Knapsack Problem

+

Traveling Salesman Problem

Problem definition

+

Given a list of cities and the distance between each pair of cities, the problem asks for the +shortest route starting at the first city, visiting each other city exactly once, then returning +to the first city. This problem is a generalization of the Hamiltonian path problem, one of Karp's +21 NP-complete problems.

+

Random problem generator

+

The class TravelingSalesmanGenerator can be used to generate random instances of this +problem. Initially, the generator creates $n$ cities $(x_1,y_1),\ldots,(x_n,y_n) \in \mathbb{R}^2$, +where $n, x_i$ and $y_i$ are sampled independently from the provided probability distributions n, +x and y. For each pair of cities $(i,j)$, the distance $d_{i,j}$ between them is set to: + +where $\gamma_{i,j}$ is sampled from the distribution gamma.

+

If fix_cities=True is provided, the list of cities is kept the same for all generated instances. +The $gamma$ values, and therefore also the distances, are still different.

+

By default, all distances $d_{i,j}$ are rounded to the nearest integer. If round=False +is provided, this rounding will be disabled.

+

Challenge A

+
    +
  • Fixed list of 350 cities in the $[0, 1000]^2$ square
    • +
  • $\gamma_{i,j} \sim U(0.95, 1.05)$
    • +
  • 500 training instances, 50 test instances
    • +
+
TravelingSalesmanGenerator(x=uniform(loc=0.0, scale=1000.0),
+                           y=uniform(loc=0.0, scale=1000.0),
+                           n=randint(low=350, high=351),
+                           gamma=uniform(loc=0.95, scale=0.1),
+                           fix_cities=True,
+                           round=True,
+                          )
+
+ +

alt

+

Multidimensional 0-1 Knapsack Problem

+

Problem definition

Given a set of $n$ items and $m$ types of resources (also called knapsacks), the problem is to find a subset of items that maximizes profit without consuming more resources than it is available. More precisely, the problem is:

-where $\gamma_{i,j}$ is sampled from the distribution gamma.

-

If fix_cities=True is provided, the list of cities is kept the same for all generated instances. -The $gamma$ values, and therefore also the distances, are still different.

-

By default, all distances $d_{i,j}$ are rounded to the nearest integer. If round=False -is provided, this rounding will be disabled.